A student of E. Arthur Milne at Oxford, Thomas Cowling did research with Sydney Chapman at Imperial College, London and taught applied mathematics at the universities of Wales (University College Swansea), Dundee, Manchester, and Bangor. From 1948 until his death he was at the University of Leeds, from which he retired in 1970. His early work on stellar structure included studies of convection and radiation in transporting stellar energy and the stability of stars. He was first to compute a stellar model (the “Cowling model”) with a convective core and a radiative envelope. This work paralleled that of Ludwig Biermann, with whom he sometimes collaborated by correspondence. Later Cowling studied sunspots and developed much of the theory of magnetic fields in stars and magnetospheres, including the Sun-Earth connection. He wrote several influential books in applied mathematics.